Multivariate Methods for Clustered Binary Data With More Than One Level of Nesting.

Clustered data occur frequently in statistical practice. In some areas of application, such as ophthalmology, clustered data are the rule rather than the exception. In this setting, standard multivariate methods such as logistic regression are invalid, because of the lack of independence among outcomes for individual sample points within a cluster. In Rosner (1984), a polychotomous logistic regression model was presented to control for the effect of both cluster and individual-specific covariates while accounting for the correlation among units within a cluster. This model reduces to a beta-binomial model in the absence of covariates, and to an ordinary logistic model for clusters of size 1 and for larger clusters when no correlation is present. A 1 level of nesting correlation structure is assumed, as is typically found in ophthalmology, where the person is the cluster and the individual eyes are the units within a cluster. In this article, this model is generalized to a 2 level of nesting structure. This model is motivated by an ophthalmologic application, where data are collected in family units and one wishes to model simultaneously the correlation at the first level of nesting among persons within a family, and at the second level of nesting between eyes within a person. In the absence of covariates, the model is characterized by a compound beta-binomial distribution that generalizes the betabinomial distribution to more than one level of nesting. The compound beta-binomial distribution is then augmented in a regression setting, to allow for the presence of family-, person-, and eye-specific covariates while controlling for correlation at each level of nesting. Extensions to more than two levels of nesting are also considered. [ABSTRACT FROM AUTHOR]